Question

The product of two number is 300 and the sum of their square is 625 what is the sum of the numbers

Answer 1

Answer:

5

Step-by-step explanation:

product 300

x plus y whole square is 625

(x+y)whole square + 2xy is equal to 625

x+y whole square + 600 is equal to 625

then x+y whole square is 25

x+5is equal to root 25

then x+y is 5

Answer 2

Given,

The product of two numbers = 300

The sum of their squares = 625.

To find,

The sum of the two numbers.

Solution,

The sum of the two numbers will be 35.

We can easily solve this problem by following the given steps.

Now, let's take the two numbers to be x and y.

According to the question,

The product of two numbers = 300

xy = 300 ---- equation 1

The sum of their squares = 625

x² + y² = 625 --- equation 2

We know that (x+y)² is x² + y² + 2xy.

(x+y)² = x² + y² + 2xy

(x+y)² - 2xy = x² + y² --- equation 3 (Moving 2xy from the right-hand side to the left-hand side will result in the change of the sign from plus to minus.)

Now, putting the value of (x² + y²) from equation 3 in equation 2,

x² + y² = 625 --- equation 2

(x+y)² - 2xy = 625

(x+y)² - (2 × 300) = 625 [ Putting the value of xy from equation 1]

(x+y)² - 600 = 625

(x+y)² = 625 + 600

(x+y)² = 1225

(x+y) = √1225

(x+y) = 35

Hence, the sum of the two numbers is 35.